A cone is constructed with a semicircular piece of paper, with radius 10. Find the height of the cone.
Problem
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Tags: geometry, 3D geometry, geometry proposed
GlassBead
26.04.2012 04:11
We can see that the circumference of the base of the cone is clearly $10\pi$, and that the slant is $10$. This yields that the radius of the base is $5$, so the height is $5\sqrt{3}$. Edit: typo fixed
tc1729
29.04.2012 06:29
LOL what this is an IMO TST problem???????
batter8642
29.04.2012 18:08
It is the TST for CentroAmerican Olympiad, IberoAmerican Olympiad, and IMO.
Vo Duc Dien
30.04.2012 23:03
Should be $ 5\sqrt{3} $
primesarespecial
25.12.2020 11:37
To form a cone,pin it at the midpoint And then Join the opposite ends of the diameter.Hence the semicircular arc forms the base of the cone.The arc has a length of 10.pi. Now the base of the cone has a radius of 5. And the slant height has length equal to the radius of the semicircle .Apply the pythagoras theorem to get that The height is sqrt(75)=5.sqrt(3)